Answer:
Step-by-step explanation:
To write an exponential equation in the form
�
=
�
�
�
y=ab
x
, you can use the given points
(
−
3
,
24
)
(−3,24) and
(
−
2
,
12
)
(−2,12). Substitute these values into the equation to form a system of equations. Let's solve for
�
a and
�
b:
For the point
(
−
3
,
24
)
(−3,24):
24
=
�
�
−
3
24=ab
−3
For the point
(
−
2
,
12
)
(−2,12):
12
=
�
�
−
2
12=ab
−2
Now, you have a system of two equations with two variables. You can use these equations to solve for
�
a and
�
b. Let's solve it step by step:
From the first equation:
24
=
�
�
−
3
24=ab
−3
Divide both sides by
�
−
3
b
−3
:
24
�
3
=
�
24b
3
=a
Now, substitute this expression for
�
a into the second equation:
12
=
(
24
�
3
)
�
−
2
12=(24b
3
)b
−2
Combine the exponents on
�
b:
12
=
24
�
12=24b
Divide both sides by 24:
�
=
1
2
b=
2
1
Now that you have the value of
�
b, substitute it back into the expression for
�
a:
�
=
24
�
3
=
24
(
1
2
)
3
=
24
⋅
1
8
=
3
a=24b
3
=24(
2
1
)
3
=24⋅
8
1
=3
So, the exponential equation in the form
�
=
�
�
�
y=ab
x
is:
�
=
3
(
1
2
)
�
y=3(
2
1
)
x
